Skip to main content

Full text of "Treatise On Analysis Vol-Ii"

See other formats


x       NOTATION

Zp                                                set of p-adic integers: 12.9, Problem 4

Tp                                                /7-adic solenoid: 12.9, Problem 4

G/H, H\G                                    homogeneous space of left (right) cosets

of a subgroup H in a group G: 12.10

and 12.11
G  A                                           union of the orbits of the points of a

subset A of E, with respect to an action of

G on E: 12.10

E/G                                             space of orbits with respect to G: 12.10

^C(X)                                           space   of   continuous   complex-valued

functions on X: 12.14
E/F                                              quotient normed space of a normed space

E by a vector subspace F: 12.14
(x, x'y, <#', jc>                              x'(x) for a vector x  E and a continuous

linear form x' e E' (the dual of E): 12.15
*u                                                 transpose of a continuous linear map-

ping: 12.15
U(E)                                             unitary group of a Hilbert space E : 12. 1 5,

Problem 8
^*(X; K), Pfc(X; K)                      space   of   continuous   complex- valued

functions with support contained in the

compact subset K of X: 13.1
Jf (X), JTC(X)                               space   of   continuous   complex-valued

functions on X with compact support:

13.1

sx                                                 Dirac measure at the point x: 13.1

g  \i                                             measure with density g with respect to /i :

13.1 and 13.13
n(p)                                                    image of a measure JJL under a proper con-

tinuous   mapping   n:   13.1   and   13.1,

Problem 8
A*u > fl I U                                             measure induced on an open set U by a

measure \JL (or restriction of $ to U): 13.1
MC(X), M(X)                                     space of complex measures on X: 13.1

J/4<, J/(*) 44X)                     integral of/eJf(X) with respect to /*:

13.1

Jf R(X; K)                                   space of continuous real-valued functions

with support contained in the compact
subset K of X: 13.2